 
Summary: Statistical mechanical theory for steady state systems. VI.
Variational principles
Phil Attarda
School of Chemistry F11, University of Sydney, New South Wales 2006, Australia
Received 15 August 2006; accepted 31 October 2006; published online 1 December 2006
Several variational principles that have been proposed for nonequilibrium systems are analyzed.
These include the principle of minimum rate of entropy production due to Prigogine Introduction
to Thermodynamics of Irreversible Processes Interscience, New York, 1967 , the principle of
maximum rate of entropy production, which is common on the internet and in the natural sciences,
two principles of minimum dissipation due to Onsager Phys. Rev. 37, 405 1931 and to Onsager
and Machlup Phys. Rev. 91, 1505 1953 , and the principle of maximum second entropy due to
Attard J. Chem.. Phys. 122, 154101 2005 ; Phys. Chem. Chem. Phys. 8, 3585 2006 . The
approaches of Onsager and Attard are argued to be the only viable theories. These two are related,
although their physical interpretation and mathematical approximations differ. A numerical
comparison with computer simulation results indicates that Attard's expression is the only accurate
theory. The implications for the Langevin and other stochastic differential equations are
discussed. © 2006 American Institute of Physics. DOI: 10.1063/1.2400859
I. INTRODUCTION
Variational principles play an essential role in the physi
cal sciences. They provide both fundamental conceptual un
